J.R.. Smith received the Sixth Man Award Monday with his father, Earl, and mother, Ida, on hand — and his father says Knicks coach Mike Woodson deserved the credit for the turnaround. Photo: UPI

Earl Smith, J.R.’s father who served as his first coach growing up in Central Jersey, gave all the credit to his son’s grand emergence this season to Mike Woodson and took a swipe at his former coach in Denver, George Karl, during a wide-ranging interview yesterday.

Smith won the Sixth Man Award on Monday, capping his career season in which he became Carmelo Anthony’s star sidekick, averaging a career-best 18.1 points. Before Game 2 against Boston, Smith, long known as an underachieving renegade, received a thunderous standing ovation at the Garden when presented the trophy.

“I got to give all the credit to Knicks organization and Coach Woodson,’’ Earl Smith told The Post yesterday. “When you got a coach like that, anything’s possible.

“I noticed it from the first game,’’ Earl Smith added. “When you have all the potential in the world, there’s a certain way you have to approach him. There’s just different ways to approach different people. Woodson had the patience. The other coaches didn’t have the patience.

“If you’re a basketball player, you either can shoot and pass or you can play defense,’’ Earl continued. “Not everyone can do everything. I’m not saying this because he’s my son, but J.R. basically can do everything.’’

Earl felt Karl had it in for Smith during their five seasons together in Denver.

“The assistant coaches loved him there but they couldn’t say anything,’’ Earl Smith said. “There was negativity from Day 1. I was at the practice arena just sitting around and George comes by while J.R. is shooting. I heard George say to the assistants, ‘J.R. Smith, I’m going to bust his ass this year.’ ’’

Earl expects J.R. to opt out of his contract and become a free agent July 1. The Knicks can be outbid since the most they can offer him under the salary-cap rules for Early-Bird rights is a four-year deal starting at $5.2 million per season. Teams under the salary cap can blow the Knicks out of the water.

Earl said his son has already taken less to be a Knick, claiming the Lakers had a superior offer last summer.

“It depends on what’s on the table,’’ Earl said. “He’s already taken a lot less the last two years to play here. Whatever the decision, I support. I would love for him to be here but I have my other two sons here.’’

Chris Smith, a point guard, tore his patella tendon at Knicks training camp last October and has been rehabbing at their facility. He is a favorite to make the team next season.

Earl Smith, who lives in Millstone Township, N.J., has attended every home game this season with his wife, Ida. Earl, after a stop at a junior college, played at Monmouth University, where his youngest son, Demitrius, is now a standout nose guard and NFL prospect.

(Earl won’t be attending Game 3 in Boston tomorrow because of Demitrius’ spring football game.)

“The fans are great and it’s been an unbelievable feeling,’’ Earl said of Tuesday’s Garden serenade. “I was excited to see him succeed and everyone’s not bashing him. The announcers say it’s a good shot now. Looking back, it’s the same damn shot. It’s the same shot he’s taken for nine years.’’

Earl said J.R.’s recent admission he partied too hard in his first season in New York was spot on. Smith signed with the Knicks last February after spending the lockout playing in China.

“Coming from China he didn’t do anything for three, four months over there but eat and play,’’ Earl said. “There was no clubbing in China. Of course a young kid comes back and he got caught up with it. That whole experience humbled him, seeing how they lived.’’

The turning point for this season came in March when Smith made it his mission to attack the basket and not settle for his patented step-back jump shot that occasionally failed him.

“He’s so athletic, he could go to the basket anytime he wanted it,’’ Earl said. “But he got fouled and referees never called it. He was getting beat up and getting tired of it. I’m not bashing referees. But they get caught up watching and not reffing. I always thought that about him and Melo, too. There’s some guys you can’t even touch. Not them. Maybe it’s because everybody hates New York.’’

Earl doesn’t see Smith as a sixth man forever, especially if he leaves the Knicks.

“Every player wants to start, right down to the 15th player,’’ Smith said. “But in Woodson’s chemistry, it was different and it was working. I don’t know what it will be next season.

“He bought into the system and realized what he had to do to make this team successful,’’ Earl added. “The older guys bended his ear. When coaches, the owner, GM, Allan Houston is on your side and everybody’s pulling for you, it makes a big difference.’’